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\usepackage{epstopdf}


% %% Jose Antonio Abell Mena provided this for DSL descriptions
% % (used in a file _Chapter_SoftwareHardware_Domain_Specific_Language_English.tex
% % This is added for listing FEI DSL
% %   since   he   customized   it,   it   needs   to   be   changed   (linked  to
% % /usr/share/texmf/tex/latex/misc)
% %\usepackage{myListings}
% \input{essi_listings_options.tex}




 
\usepackage{threeparttable}

%\usepackage{MnSymbol}%
% for smileys
\usepackage{wasysym}%
\usepackage{multirow}
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\usepackage{subfig}
\usepackage{tabularx}
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\usepackage[breakall]{truncate}
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\usepackage{ulem}
\usepackage{amsmath}
\usepackage{bm}
\usepackage{IEEEtrantools}
\usepackage{setspace}
\usepackage{scalerel}


      
\usepackage{multimedia}

% for inclusion of other PDF pages, in this case Frank's presentation
\usepackage{pdfpages}

%This is a macro to  convert eps to pdf files on the fly.
% make sure figure syntax uses graphicx syntax NOT epsfig syntax
%from http://mailman.mit.edu/pipermail/macpartners/2005-January/000780.html
%
% \ifx\pdfoutput\undefined
% % we are running LaTeX, not pdflatex
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% \else
% % we are running pdflatex, so convert .pdf files to .pdf
% \usepackage[pdftex]{graphicx}
% \usepackage{epstopdf}
% \fi
% %*****************************************


%% ovo je za cirilicu
\input vuk.def
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\newfont{\cyrjbnaslov}{wncyss10 scaled 1400 }



% % for not showing eq numbers unless eq is references
% \usepackage[fleqn,tbtags]{mathtools}
% \mathtoolsset{
%   showonlyrefs
%   }

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% FEI  LOGO definition
\newcommand{\FEI}
{{\sf \uppercase{F}\kern-0.20em\uppercase{E}\kern-0.20em\uppercase{I}}}

% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % % ovo je za cirilicu
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\setbeamertemplate{navigation symbols}{}
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%  \usetheme{Marburg} % ima naslov i sadrzaj sa desne strane
%  \usetheme{Hannover} % ima naslov i sadrzaj sa leve strane
%  \usetheme{Singapore} % ima sadrzaj i tackice gore
%  \usetheme{Antibes}  % ima sadrzaj gore i kao graf ...
%  \usetheme{Berkeley} % ima sadrzaj desno
%  \usetheme{Berlin} % ima sadrzaj gore i tackice
%  \usetheme{Goettingen} % ima sadrzxaj za desne strane
%  \usetheme{Montpellier} % ima graf sadrzaj gore
%  \usetheme{Warsaw}
%  \usetheme{Warsaw}
  \usetheme{Dresden}
    \usecolortheme[RGB={20,0,128}]{structure}

% or ...

  \setbeamercovered{transparent}


%  \setbeamercovered{transparent}
% or whatever (possibly just delete it)
%  \usecolortheme{albatross} % teget sa svetlim slovima
%  \usecolortheme{beetle} % siva pozadina (vrh plav)
  \usecolortheme{seagull} % sivo
%%%%%%%
%  \usecolortheme{BorisJeremic}
%%%%%%%
%  \usecolortheme{rose}
%   \usefonttheme[onlylarge]{structuresmallcapsserif}
%   \usefonttheme{structuresmallcapsserif}
}

\definecolor{mycolor}{rgb}{0,0.08,0.45}%


\usepackage[greek,english]{babel}



\usepackage{amsmath}
\usepackage{mathrsfs}
\usepackage{amsfonts}

\newcommand{\ud}{{\rm d}}


\usepackage{array}



%%%%  HYPERREF  HYPERREF  HYPERREF  HYPERREF  HYPERREF
%%%%  HYPERREF  HYPERREF  HYPERREF  HYPERREF  HYPERREF
\definecolor{webgreen}{rgb}{0, 0.35, 0} % less intense green
\definecolor{webblue}{rgb}{0, 0, 0.50} % less intense blue
\definecolor{webred}{rgb}{0.35, 0, 0} % less intense red
%\usepackage[colorlinks=true,linkcolor=webblue,citecolor=webred,urlcolor=webgreen]{hyperref}


\usepackage{hyperref}
\hypersetup{
  pdfmenubar=true,
  pdftoolbar=true,
  pdfpagemode={None}
             colorlinks=true,
             linkcolor=webblue,
             citecolor=webblue,
             urlcolor=webblue,
}
% \usepackage[pdfauthor={Boris Jeremic},
%             colorlinks=true,
%             linkcolor=webblue,
%             citecolor=webblue,
%             urlcolor=webblue,
%             linktocpage,
%             pdftex]{hyperref}


\usepackage{pause}
% or whatever
%\usepackage{html}
%\usepackage{url}

\usepackage[latin1]{inputenc}
% or whatever
\usepackage{times}
\usepackage[T1]{fontenc}
% Or whatever. Note that the encoding and the font should match. If T1
% does not look nice, try deleting the line with the fontenc.



%      Site Specific Dynamics of Structures: 
%From Seismic Source to 
%the Safety of Occupants and Content


\title[Real-ESSI]
        {Nuclear Installation Lifecycle: \\
Modeling and Simulation of 														 \\
Design Basis and Beyond Design Basis					 \\
ESSI Behavior
}


%\subtitle
%{Include Only If Paper Has a Subtitle}

%\author[Author, Another] % (optional, use only with lots of authors)
%{F.~Author\inst{1} \and S.~Another\inst{2}}
% - Give the names in the same order as the appear in the paper.
% - Use the \inst{?} command only if the authors have different
%   affiliation.
\pgfdeclareimage[height=0.2cm]{university-logo}{/home/jeremic/BG/amblemi/ucdavis_logo_blue_sm}
\pgfdeclareimage[height=0.7cm]{lbnl-logo}{/home/jeremic/BG/amblemi/lbnl-logo}


\author[Jeremi{\'c} et al.] % (optional, use only with lots of authors)
%{Boris~Jeremi{\'c}}
{Yuang Feng, Han Yang, Hexiang Wang, Fangbo Wang, \\
\vspace*{2mm}
Boris Jeremi{\'c}
}

%\institute[Computational Geomechanics Group \hspace*{0.3truecm}
\institute[\pgfuseimage{university-logo}\hspace*{0.1truecm}\pgfuseimage{lbnl-logo}] % (optional, but mostly needed)
%{ Professor, University of California, Davis\\
{ University of California, Davis, CA\\
%  and\\
%  Faculty Scientist, Lawrence Berkeley National Laboratory, Berkeley }
  Lawrence Berkeley National Laboratory, Berkeley, CA}
% - Use the \inst command only if there are several affiliations.
% - Keep it simple, no one is interested in your street address.


\date[] % (optional, should be abbreviation of conference name)
{\small SMiRT25\\
         Charlotte, NC, USA, August 2019}

\subject{}
% This is only inserted into the PDF information catalog. Can be left
% out.



% If you have a file called "university-logo-filename.xxx", where xxx
% is a graphic format that can be processed by latex or pdflatex,
% resp., then you can add a logo as follows:

%\pgfdeclareimage[height=0.2cm]{university-logo}{/home/jeremic/BG/amblemi/ucdavis_logo_gold_lrg}
%\logo{\pgfuseimage{university-logo}}

% \pgfdeclareimage[height=0.5cm]{university-logo}{university-logo-filename}
% \logo{\pgfuseimage{university-logo}}




% Delete this, if you do not want the table of contents to pop up at
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% \AtBeginSubsection[]
\setcounter{tocdepth}{3}
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 }


% If you wish to uncover everything in a step-wise fashion, uncomment
% the following command:





\begin{document}

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\begin{frame}
  \titlepage
\end{frame}

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\begin{frame}
  \frametitle{Outline}

   \begin{scriptsize}
  \tableofcontents
% You might wish to add the option [pausesections]
   \end{scriptsize}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Structuring a talk is a difficult task and the following structure
% may not be suitable. Here are some rules that apply for this
% solution:

% - Exactly two or three sections (other than the summary).
% - At *most* three subsections per section.
% - Talk about 30s to 2min per frame. So there should be between about
%   15 and 30 frames, all told.

% - A conference audience is likely to know very little of what you
%   are going to talk about. So *simplify*!
% - In a 20min talk, getting the main ideas across is hard
%   enough. Leave out details, even if it means being less precise than
%   you think necessary.
% - If you omit details that are vital to the proof/implementation,
%   just say so once. Everybody will be happy with that.



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Introduction}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\subsection{\ }



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%





 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Motivation}

\begin{itemize}



 

%\vspace*{0.3cm}
  \item[]  Improve  modeling  and  simulation  for  infrastructure objects
 

\vspace*{2mm}
 \item[]  Expert numerical modeling and simulation tool

% \vspace*{1mm}
%   \item[]      Use of numerical models to
%   analyze statics and dynamics of soil/rock-structure systems
% 

\vspace*{2mm}
  \item[]  Control and reduce  modeling uncertainty

%\vspace*{1mm}
%  \item[]  Choice of analysis level of sophistication


\vspace*{2mm}
  \item[] Goal: Predict and Inform rather than fit

\vspace*{2mm}
  \item[] Engineer needs to know!



%
%  
%  
%  \vspace*{1mm}
%    \item[]  Follow  the  flow, input and dissipation,  of seismic  energy, 

\vspace*{2mm}
  \item[]  System  for modeling and simulation of
  Earthquakes and/or    Soils and/or    Structures    and    their    Interaction:\\
   Real-ESSI, 
 \vspace*{2mm}
% %  \hspace*{25mm} 
     { \bf \url{http://real-essi.info/} }
% %  \hspace*{25mm} 
%    \url{http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/}
%    \href{http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/}{{http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/}
%  % \url{http://ms-essi.info/}
%  





\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  







                       

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Prediction under Uncertainty}


\begin{itemize}




%\vspace*{1mm}
  \item    \underline{Modeling Uncertainty}, Simplifying assumptions
    \begin{itemize}

\vspace*{2mm}
      \item[] Low, medium, high  sophistication modeling and simulation


\vspace*{2mm}
      \item[] Choice of sophistication level for confidence in  results

    \end{itemize}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\vspace*{4mm}
  \item   \underline{Parametric    Uncertainty},  ${M}  \ddot{u_i}  +  {C}  \dot{u_i} + {K}^{ep} {u_i} = {F(t)}$,

  \begin{itemize}

\vspace*{2mm}
    \item[] Uncertain mass $M$, viscous damping  $C$ and stiffness $K^{ep}$


\vspace*{2mm}
    \item[] Propagation  of uncertainty in  loads, $F(t)$


\vspace*{2mm}
    \item[] Results are PDFs   and   CDFs  for  $\sigma_{ij}$,  $\epsilon_{ij}$,  $u_i$,  $\dot{u}_i$,  $\ddot{u}_i$

  \end{itemize}




\end{itemize}



% 
% 
% %Le doute n'est pas un {\'e}tat bien agr{\'e}able,\\ 
%        mais l'assurance est un {\'e}tat ridicule.  (Fran{\c c}ois-Marie Arouet, Voltaire)



\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Modeling Uncertainty}

\begin{itemize}



  \item[-]  Important (?!)  features are simplified, 1C vs 3C, inelasticity

%\vspace*{4mm}
%     \item   Unrealistic   and   unnecessary  modeling simplifications

\vspace*{1mm}
     \item[-]  Modeling  simplifications   are  justifiable  if  one  or  two 
     level higher sophistication model demonstrates that features being
     simplified out are not important



\end{itemize}


% local
%\vspace*{-2mm}
\begin{center}
\hspace*{-7mm}
%\movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
\movie[label=show3,width=5.5cm,poster,autostart, showcontrols]
  {\includegraphics[width=50mm]
  {/home/jeremic/tex/works/Conferences/2016/IAEA_TecDoc_February2016/My_Current_Work/movie_2_npps_mp4_icon.jpeg}}
  {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Model01_ESSI_Response_May2015/movie_2_npps.mp4}
%
%\hfill
\hspace*{-5mm}
%
\movie[label=show3,width=6.0cm,poster,autostart,showcontrols]
  {\includegraphics[width=50mm]
  {/home/jeremic/tex/works/Conferences/2017/SMiRT_24/present/3D_Nonlinear_Modeling_and_it_Effects/NPP_Plastic_Dissipation_grab.jpg}}
  {/home/jeremic/tex/works/Thesis/HanYang/Files_10Aug2017/NPP_Plastic_Dissipation.mp4}
\hspace*{-7mm}
%\end{flushleft}
%%
\end{center}
% local

% % \vspace*{-5mm}
% \begin{center}
% %\begin{flushleft}
% % \hspace*{-15mm}
% \movie[label=show3,width=5cm,poster,autostart,showcontrols]
% {\includegraphics[width=5cm]
% {/home/jeremic/tex/works/Conferences/2017/SMiRT_24/present/3D_Nonlinear_Modeling_and_it_Effects/NPP_Plastic_Dissipation_grab.jpg}}
% {/home/jeremic/tex/works/Thesis/HanYang/Files_10Aug2017/NPP_Plastic_Dissipation.mp4}
% %\end{flushleft}
% %%
% \hfill
% %%
% %\begin{flushright}
% % \hspace*{-15mm}
% \movie[label=show3,width=5cm,poster,autostart,showcontrols]
% {\includegraphics[width=5cm]
% {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/SMR_Energy_Dissipation_screen_grab.jpg}}
% {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/SMR_Energy_Dissipation.mp4}
% %\end{flushright}
% \end{center}
%  



\end{frame}




      
%OVDE

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{Modeling Uncertainty, 6C vs 1C Motions}
% 
%      
% % local
% \vspace*{-2mm}
% \begin{center}
% \hspace*{-7mm}
% %\movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
% \movie[label=show3,width=8.8cm,poster, showcontrols]
%   {\includegraphics[width=92mm]
%   {/home/jeremic/tex/works/Conferences/2016/IAEA_TecDoc_February2016/My_Current_Work/movie_2_npps_mp4_icon.jpeg}}
%   {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Model01_ESSI_Response_May2015/movie_2_npps.mp4}
% \end{center}
% % local
% %  \vspace*{-2mm}
% %  \begin{center}
% %  \hspace*{-7mm}
% %  \movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
% %    {\includegraphics[width=90mm]{movie_2_npps_mp4_icon.jpeg}}{movie_2_npps.mp4}
% %  \end{center}
% 
% 
% % online
% \vspace*{-12mm}
% \begin{flushleft}
% %\vspace*{-15mm}
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_2_npps.mp4}
%   {\tiny (MP4)}
% \end{flushleft}
% % online
% 
% 
% 
% 
% 
% \end{frame}
% 





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Parametric Uncertainty: Soil Stiffness and Strength}


\vspace*{2mm}
%\vspace*{-3mm}
\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{-7mm}
\includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/YoungModulus_RawData_and_MeanTrend_01-Ed.pdf}
\hspace*{-3mm}
% \hfill
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/YoungModulus_Histogram_Normal_01-Ed.pdf}
%
\end{center}
\end{figure}

\vspace*{-5mm}
\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{-7mm}
\includegraphics[width=5.00truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/ShearStrength_RawData_and_MeanTrend-Mod.pdf}
\hspace*{-3mm}
% \hfill
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/ShearStrength_Histogram_PearsonIV-FineTuned-Mod.pdf}
%
\end{center}
\end{figure}

%\vspace*{-5mm}
%\vspace*{-1.8cm}
%\hspace*{-3.3cm}
\begin{flushright}
{\tiny
(cf. Phoon and Kulhawy (1999B))\\
~}
\end{flushright}
%


\end{frame}

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Parametric Uncertainty: Material Properties}
% 
%           
% 
% \vspace*{5mm}
% \begin{figure}[!hbpt]
% \begin{center}
% % %
% \hspace*{-3mm}
% \includegraphics[width=2.5truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldPhiPdf.pdf}
% \hspace*{-3mm}
% \includegraphics[width=2.5truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldPhiCdf.pdf}
% \hspace*{3mm}
% \includegraphics[width=2.5truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldSuPdf.pdf}
% \hspace*{-3mm}
% \includegraphics[width=2.5truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldSuCdf.pdf}
% \\
% %\vspace*{-2mm}
% \hspace*{-2.5cm} \mbox{\tiny Field $\phi$} \hspace*{3.5cm} \mbox{\tiny Field $c_u$}
% \\
% \vspace*{10mm}
% \hspace*{-3mm}
% \includegraphics[width=2.5truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabPhiPdf.pdf}
% \hspace*{-3mm}
% \includegraphics[width=2.5truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabPhiCdf.pdf}
% \hspace*{3mm}
% \includegraphics[width=2.5truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabSuPdf.pdf}
% \hspace*{-3mm}
% \includegraphics[width=2.5truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabSuCdf.pdf}
% \\
% %\vspace*{-8mm}
% \hspace*{-2.5cm} \mbox{\tiny Lab $\phi$} \hspace*{3.5cm} \mbox{\tiny Lab $c_u$}
% \end{center}
% \end{figure}
% 
% 
% 
% \end{frame}
% 






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%- 
%- 
%- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%- \begin{frame} 
%- 
%- \frametitle{Real-ESSI Simulator System}
%- 
%- The  Real-ESSI, 
%- {\underline {\bf Real}}istic  
%- %{\underline {\bf M}}odeling  and  
%- %{\underline {\bf S}}imulation  of  
%- {M}odeling  and  
%- {S}imulation  of  
%- {\underline {\bf E}}arthquakes,  
%- {\underline {\bf S}}oils,
%- {\underline {\bf S}}tructures  and  their  
%- {\underline {\bf I}}nteraction.  Simulator  is  a  software,  hardware  and
%- documentation   system   for   time  domain,
%- linear  and  nonlinear,  inelastic,  deterministic  or probabilistic, 3D, finite
%- element modeling and simulation of:
%- 
%-     \begin{itemize}
%- %\vspace*{1mm}
%-       \item statics and dynamics of soil,
%- %\vspace*{1mm}
%-       \item    statics and dynamics of rock,
%- %\vspace*{1mm}
%-       \item    statics and dynamics of structures,
%- %\vspace*{1mm}
%-       \item    statics of soil-structure systems, and
%- %\vspace*{1mm}
%-       \item    dynamics of earthquake-soil-structure system interaction
%-     \end{itemize}
%- 
%- 
%- 
%- Used for:
%- \begin{itemize}
%- %\vspace*{1mm}
%-   \item Design, linear elastic, load combinations, dimensioning
%- 
%- 
%- %\vspace*{1mm}
%-   \item Assessment, nonlinear/inelastic, safety margins
%- \end{itemize}
%- 
%- 
%- 
%- 
%- \end{frame}
%- 
%- 
%- 
%- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%- \begin{frame} 
%- 
%- \frametitle{Real-ESSI Simulator System}
%- 
%-  
%- \begin{itemize}
%- 
%- 
%-   \item Real-ESSI System Components
%-     \begin{itemize} 
%-      \item Real-ESSI Pre-processor (gmsh/gmESSI, X2ESSI) 
%-      \item Real-ESSI Program (local, remote, cloud)
%-      \item Real-ESSI Post-Processor (Paraview, Python, Matlab)
%- 
%-     \end{itemize} 
%- 
%- \vspace*{1mm}
%-   \item Real-ESSI System availability:                   
%-     \begin{itemize}
%- %\vspace*{1mm}
%-      \item Educational  Institutions: Amazon Web Services (AWS), free 
%-      \item Government Agencies, National Labs: AWS GovCloud
%-      \item Professional  Practice: AWS, commercial
%- %\vspace*{1mm}
%- %%\vspace*{1mm}
%- %      \item Sources available to collaborators
%-     \end{itemize}
%- 
%- 
%- 
%- \vspace*{1mm}
%-   \item Real-ESSI Short Courses, online, worldwide
%- 
%- 
%- 
%- \vspace*{1mm}
%-   \item System description and documentation at  
%-     \url{http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/}
%- %
%- %\url{http://real-essi.info/}
%- %
%- 
%- 
%- % \vspace*{2mm}
%- %   \item
%- % 
%- 
%- 
%- \end{itemize}
%- 
%- 
%- \end{frame}
%- 
%- 
%- 
%- 







































%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Modeling and Simulation of ESSI for Nuclear Installations}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{\ }



%






 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Regional Geophysical  Models}

\begin{itemize}

  \item Free Field seismic motions on regional scale


\vspace*{4mm}
  \item Knowledge of geology (deep and shallow) needed


\vspace*{4mm}
 \item Developed using SW4 and/or Real-ESSI


\vspace*{4mm}
  \item  Collaboration  with LLNL: Dr.~Rodgers, Dr.~Pitarka and Dr.~Petersson




\end{itemize}
 
\end{frame}


 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Regional Geophysical  Models}

 \begin{figure}[!htb]
 \begin{center}
  \includegraphics[width=5truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/San_Francisco__Regional_Model_BIG.jpg}
  \includegraphics[width=5.2truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/San_Francisco__Regional_Model.jpg}
 \end{center}
% \caption{\label{Fig:NPP_Model_In_Real_ESSI} Nuclear Power Plant Model with Shallow Foundation }
 \end{figure}

Rodgers and Pitarka 

\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Regional Geophysical  Models}

 \begin{figure}[!htb]
 \begin{center}
  \includegraphics[width=10truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/USG-Bay_Area_Model_CC_det2_sm.jpg}
 \end{center}
% \caption{\label{Fig:NPP_Model_In_Real_ESSI} Nuclear Power Plant Model with Shallow Foundation }
 \end{figure}

USGS
 
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%




%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%  \frametitle{Example Regional Model}
%  
%   \begin{figure}[!htb]
%   \begin{center}
%    \includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/Vs_at_top.jpg}
%  %  \includegraphics[width=5truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/Horizontal_Velocity_at_12s.jpg}
%    \includegraphics[width=5truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/Peak_Velocity.jpg}
%   \end{center}
%  % \caption{\label{Fig:NPP_Model_In_Real_ESSI} Nuclear Power Plant Model with Shallow Foundation }
%   \end{figure}
%   
%  \end{frame}
%  
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Example Regional Model (Rodgers)}




  
%\vspace*{5mm}
\begin{center}
%\hspace*{-5mm}
%
%\movie[label=show3,width=10.0cm,poster,autostart,showcontrols]
\movie[label=show3,width=8.0cm,poster]
%\movie[label=show3,width=6.0cm,poster,showcontrols]
  {\includegraphics[width=80mm]{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/NPP_animations_August2017/M6_5_s500_BASIN_STOCHASTIC_mag_SLOW.jpg}}
     {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/NPP_animations_August2017/M6_5_s500_BASIN_STOCHASTIC_mag_SLOW.mpg}
\hspace*{-5mm}
%
\end{center}


% online   
\vspace*{-5mm}
\begin{flushleft}
\hspace*{-5mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/NPP_animations_August2017/M6_5_s500_BASIN_STOCHASTIC_mag_SLOW.mpg}
  {\tiny (MP4)}
%\hspace*{-5mm}
\end{flushleft}
% online






% out 
% out %\vspace*{-2mm}
% out \begin{center}
% out \hspace*{-15mm}
% out %
% out \movie[label=show3,width=8.0cm,poster,autostart,showcontrols]
% out   {\includegraphics[width=60mm]{BJicon.png}}{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/M6.5_s500_BASIN+STOCHASTIC.mag.SLOW.mpg}
% out \hspace*{-15mm}
% out %
% out \end{center}
% out 
% out 
% out \begin{flushleft}
% out \vspace*{-15mm}
% out \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/Rodgers_Free_Field_motions/M6.5_s500_BASIN+STOCHASTIC.mag.SLOW.mpg}
% out %  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
% out   {\tiny (MP4)}
% out \end{flushleft}
% out %
% out 


\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Energy Input and Dissipation}

\begin{itemize}

\vspace*{1mm}
     \item[] Energy input, dynamic forcing


\vspace*{4mm}
     \item[] Energy dissipation outside SSI domain:
       \begin{itemize}
         \item[] SSI system oscillation radiation
         \item[] Reflected wave radiation
       \end{itemize}
%\vspace*{1mm}
     \item[] Energy dissipation/conversion inside SSI domain:
       \begin{itemize}
         \item[] Inelasticity of soil, contact zone, structure, foundation, dissipators
         \item[] Viscous coupling with internal/pore fluids, and external fluids
% %         \item[] potential and kinetic energy
%          \item[] potential $\leftarrow \! \! \! \! \! \! \rightarrow$ kinetic energy
       \end{itemize}                           



%\vspace*{1mm}
%   \item[] Numerical energy dissipation (numerical damping/production and period  errors)
%   \item[] Numerical energy dissipation (damping/production)
   \item[] Numerical energy dissipation/production


\end{itemize}

%
\end{frame}
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 
\frametitle{Plastic Energy Dissipation}


\vspace*{2mm}
 
 Single elastic-plastic element under cyclic shear loading
 
\begin{itemize}
\item[] Difference between plastic work and plastic dissipation
\item[] Plastic work can decrease
\item[] Plastic dissipation always increases
\end{itemize}
 
%\vspace*{-7mm}
\begin{figure}[!hbpt]
\begin{center}
\hspace*{-5mm}
\includegraphics[width=11.0truecm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Dissipation_Material.png}
\end{center}
\end{figure}
  
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%




% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% 
% \frametitle{Energy Dissipation Control Mechanisms}
% 
% \begin{figure}[!H]
% %\hspace*{-10mm}
%      \includegraphics[width=3.4cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_plasticity.pdf}
%      \includegraphics[width=3.4cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_Rayleigh.pdf}
%      \includegraphics[width=3.4cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_Newmark.pdf}
% \end{figure}
% 
% 
% % \hspace*{10mm} Numerical  \hspace*{20mm}  Viscous  \hspace*{20mm} Plasticity 
%  \hspace*{10mm} Plasticity \hspace*{20mm}  Viscous  \hspace*{20mm} Numerical
% 
% 
% 
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}

\frametitle{Energy Dissipation Control}

\begin{figure}[!H]
%\hspace*{-10mm}
%     \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_a.pdf}
%     \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_b.pdf}
     \includegraphics[width=9cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_g.pdf}
%     \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_e.pdf}
\end{figure}




\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Inelastic Modeling of Soil Structure Systems}

\begin{itemize}

%\vspace*{1mm}
     \item Soil, inelastic, elastic-plastic
       \begin{itemize}
         \item[] Dry, single phase
         \item[] Unsaturated, partially saturated
         \item[] Fully saturated
       \end{itemize}


%\vspace*{1mm}
     \item Contact, inelastic, soil/rock -- foundation
       \begin{itemize}
         \item[]  Dry,  single  phase,  
           \begin{itemize}
             \item[]  Normal, hard  and  soft, gap open/close
             \item[]  Friction, nonlinear
           \end{itemize}
         \item[] Fully saturated, suction, excess pressure, buoyant force
       \end{itemize}


%\vspace*{1mm}
     \item Structure, inelastic, damage, cracks
       \begin{itemize}
         \item[] Nonlinear/inelastic 1D reinforced concrete fiber beam
         \item[] Nonlinear/inelastic 3D reinforced concrete solid element
         \item[] Alcali Silica Reaction concrete modeling
       \end{itemize}


%%\vspace*{1mm}
%     \item Fluid-Solid interaction (open surface)



\end{itemize}

%
\end{frame}


% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% 
%  \frametitle{NPP Model }
% 
%   \begin{figure}[!h]
%   \begin{center}
%    \includegraphics[width=8.5cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/NPP_With_Shallow_Foundation.pdf}
%   \end{center}
% %  \caption{\label{Fig:NPP_Model_In_Real_ESSI} Nuclear Power Plant Model with Shallow Foundation }
%   \end{figure}
% 
% 
% % \begin{tikzpicture}[remember picture,overlay]
% %     \node[xshift=3.5cm,yshift=-0.6cm] at (current page.center) {\includegraphics[width=0.5\textwidth]{images/Contact_In_Industry}};
% % \end{tikzpicture}
% 
% \end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% 
%  \frametitle{Structure Model}
% 
%  The nuclear power plant structure comprise of
%  \begin{itemize}
%   \item Auxiliary building, $f^{aux}_{1}= 8Hz$
%   \item Containment/Shield building, $f^{cont}_{1}= 4Hz$
%   \item Concrete raft foundation: $3.5m$ thick
%  \end{itemize}
%   \begin{figure}[!h]
%   \begin{center}
%    \includegraphics[width=0.8\textwidth]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/NPP_Model_Auxiliary_And_Containment_Building.pdf}
%   \end{center}
%   \caption{\label{Fig:NPP_Structure_Model_In_Real_ESSI} Auxiliary and Containment Building }
%   \end{figure}
% 
% \end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}

 \frametitle{Inelastic Soil and Inelastic Contact}

 \begin{itemize}
  \item Shear velocity of soil $V_s=500m/s$
  \item Undrained shear strength (Dickenson 1994) $V_s [m/s] = 23 (S_u [kPa])^{0.475}$
  \item For $V_s=500m/s$ Undrained Strength $S_u=650kPa$ and Young's Modulus of $E=1.3GPa$
  \item von Mises, Armstrong Frederick kinematic hardening
  ($S_u=650kPa$ at $\gamma=0.01\%$; $h_a = 30MPa$, $c_r = 25$)
  \item Soft contact (concrete-soil), gaping and nonlinear shear
  \end{itemize}

 \begin{figure}[!h]
 \begin{center}
  \includegraphics[width=4cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/Von_Mies_non_Linear_Hardening.pdf}
  \includegraphics[width=3.5cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/SoftContact.pdf}
 \end{center}
  \end{figure}


\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%




% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% 
%  \frametitle{Acc. Response, Top of Containment Building}
% 
%  \begin{figure}[!h]
%  \begin{center}
% \hspace*{-8mm}
%   \includegraphics[width=3.54cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/D_Acceleration_X.pdf}
%   \includegraphics[width=3.54cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/D_Acceleration_Y.pdf}
%   \includegraphics[width=3.54cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/D_Acceleration_Z.pdf}
% \\
% \hspace*{-8mm}
%   \includegraphics[width=3.54cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/FFT_D_Acceleration_X.pdf}
%   \includegraphics[width=3.54cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/FFT_D_Acceleration_Y.pdf}
%   \includegraphics[width=3.54cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/FFT_D_Acceleration_Z.pdf}
% % \caption{\label{Fig:Response_of_Top_of_Containment_Building} Seismic Response at Top of Containment Building}
%  \end{center}
% \end{figure}
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% 
%  
%  
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}

 \frametitle{Acceleration Traces, Elastic vs Inelastic }


\hspace*{-35mm}
  \begin{figure}[!h]
  \vspace*{-2mm}
  \begin{center}
  \hspace*{-15mm}
   \includegraphics[width=7.0cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/Acceleration_Elastic_Without_Contact_SMIRT_2017.pdf}
  \hspace*{-20mm}
   \includegraphics[width=7.0cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/Acceleration_Inelastic_With_Contact_SMIRT_2017.pdf}
  \hspace*{-25mm}
  \end{center}
 \end{figure}
\hspace*{-35mm}

\hspace*{10mm} Elastic  \hspace*{40mm} Inelastic \hspace*{40mm} 

\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}

 
 \frametitle{Displacement Traces, Elastic vs Inelastic}
 
\hspace*{-35mm}
  \begin{figure}[!h]
  \vspace*{-2mm}
  \begin{center}
  \hspace*{-15mm}
   \includegraphics[width=7.0cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/Elastic_Without_Contact_SMIRT_2017.pdf}
  \hspace*{-20mm}
   \includegraphics[width=7.0cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/Inelastic_With_Contact_SMIRT_2017.pdf}
  \hspace*{-25mm}
  \end{center}
 \end{figure}
\hspace*{-35mm}

\hspace*{10mm} Elastic  \hspace*{40mm} Inelastic \hspace*{40mm} 

\end{frame}
 
 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}

\frametitle{Energy Dissipation in a Large-Scale Model}

% Elastoplastic soil with contact elements
%% Both solid and contact elements dissipate energy

% \vspace*{-5mm}
\begin{center}
% \hspace*{-15mm}
\movie[label=show3,width=10cm,poster,autostart,showcontrols]
{\includegraphics[width=10cm]
{/home/jeremic/tex/works/Conferences/2017/SMiRT_24/present/3D_Nonlinear_Modeling_and_it_Effects/NPP_Plastic_Dissipation_grab.jpg}}
{/home/jeremic/tex/works/Thesis/HanYang/Files_10Aug2017/NPP_Plastic_Dissipation.mp4}
\end{center}




\begin{flushleft}
\vspace*{-15mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/NPP_Plastic_Dissipation.mp4}
%  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
  {\tiny (MP4)}
\end{flushleft}
%



\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} 

\frametitle{Uncertainty Propagation through 
Inelastic System}

% 

\begin{itemize}



\item Incremental el--pl constitutive equation
%  
    \begin{eqnarray}
    \nonumber
  \Delta \sigma_{ij} 
  = 
%  E^{EP}_{ijkl} 
     E^{EP}_{ijkl} \; \Delta \epsilon_{kl}  
     =  
     \left[
     E^{el}_{ijkl}
       -
       \frac{\displaystyle  E^{el}_{ijmn} m_{mn} n_{pq} E^{el}_{pqkl}}
           {\displaystyle n_{rs} E^{el}_{rstu} m_{tu} - \xi_* h_*}
           \right]
    \Delta \epsilon_{kl}
    \end{eqnarray}

 
  

\vspace*{3mm}
\item Dynamic Finite Elements
%
\begin{equation}
{ M} \ddot{ u_i} +
{ C} \dot{ u_i} +
{ K}^{ep} { u_i} =
{ F(t)}
    \nonumber
\end{equation}


\vspace*{3mm}
\item Material and load parameters are uncertain



\end{itemize}



\end{frame}






 
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\begin{frame}
\frametitle{Probabilistic Elastic-Plastic Modeling}


% % \vspace*{-5mm}
% \begin{center}
% % \hspace*{-15mm}
% \movie[label=show3,width=7cm,poster,autostart,showcontrols]
% {\includegraphics[width=7cm]
% {/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/NPP_Plastic_Dissipation_Density.png}}
% %{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/NPP_without_Contact_vonMises.mp4}
% {NPP_without_Contact_vonMises.mp4}
% \end{center}

%\vspace*{-5mm}
\begin{center}
% \hspace*{-15mm}
\movie[label=show3,width=9cm,poster,autostart,showcontrols]
{\includegraphics[width=9cm]
{/home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Latex/img/figure_PEP_25.png}}
% /home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Latex/img/figure_PEP_25.pdf
%{/home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Animations/PEP_Animation.mp4}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Probabilistic_Elasto_Plasticity_and_Stochastic_Elastic_Plastic_Finite_Element_Method/PEP_Animation.mp4}
\end{center}

%
% \includegraphics[width = 12cm]{./img/figure_PEP_25.pdf}


\end{frame}











%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\section[Formulation]{Stochastic Dynamic Finite Element Formulation}
%\subsection[Time domain stochastic Galerkin method]{Time domain stochastic Galerkin method}
%\frame{\tableofcontents[currentsubsection,sectionstyle=show/shaded]}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



 



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Stochastic Elastic-Plastic Finite Element Method}



\begin{itemize}

\item Material uncertainty expanded into stochastic shape funcs.
%$E(x,t,\theta) = \sum_{i=0}^{P_d} r_i(x,t) * \Phi_i[\{\xi_1, ..., \xi_m\}]$

\vspace*{1mm}
\item Loading uncertainty expanded into stochastic shape funcs.
%$f(x,t,\theta) = \sum_{i=0}^{P_f} f_i(x,t) * \zeta_i[\{\xi_{m+1}, ..., \xi_f]$

\vspace*{1mm} 
\item Displacement expanded into stochastic shape funcs.
%$u(x,t,\theta) = \sum_{i=0}^{P_u} u_i(x,t) * \Psi_i[\{\xi_1, ..., \xi_m, \xi_{m+1}, ..., \xi_f\}]$

%\item 
%Stochastic system of equation resulting from Galerkin approach (static example):
%
%\item  Time domain integration  using Newmark and/or HHT, in probabilistic spaces


\end{itemize}


\begin{tiny}
\[
%$
\begin{bmatrix}
    \sum_{k=0}^{P_d} <\Phi_k \Psi_0 \Psi_0> K^{(k)}    & \dots & \sum_{k=0}^{P_d} <\Phi_k \Psi_P \Psi_0> K^{(k)}\\
    \sum_{k=0}^{P_d} <\Phi_k \Psi_0 \Psi_1> K^{(k)}    & \dots & \sum_{k=0}^{P_d} <\Phi_k \Psi_P \Psi_1> K^{(k)}\\  \\
    \vdots & \vdots & \vdots & \vdots\\
    \sum_{k=0}^{P_d} <\Phi_k \Psi_0 \Psi_P> K^{(k)}     & \dots & \sum_{k=0}^{M} <\Phi_k \Psi_P \Psi_P> K^{(k)}
\end{bmatrix}
\begin{bmatrix}
    \Delta u_{10} \\
    \vdots \\
    \Delta u_{N0}\\
    \vdots \\
    \Delta u_{1P_u}\\
    \vdots \\
    \Delta u_{NP_u}
\end{bmatrix}
=
%\]
%\[
\begin{bmatrix}
     \sum_{i=0}^{P_f} f_i  <\Psi_0\zeta_i> \\
    \sum_{i=0}^{P_f} f_i   <\Psi_1\zeta_i> \\
   \sum_{i=0}^{P_f} f_i    <\Psi_2\zeta_i> \\
    \vdots \\
     \sum_{i=0}^{P_f} f_i  <\Psi_{P_u}\zeta_i>\\
\end{bmatrix}
%$
\]
\end{tiny}





\end{frame}








%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}
\frametitle{SEPFEM: System Size}

\begin{itemize}

  \item SEPFEM offers a complete solution (single step) 

\vspace*{2mm}
  \item  It is NOT based on Monte Carlo approach

\vspace*{2mm}
  \item  System of equations does grow (!)

\end{itemize}


\vspace*{4mm}
%   \normalsize{Typical number of terms required for a SEPFEM problem} \vspace{1cm}\\
  \scalebox{0.7}{
  \begin{tabular}{ c c c c}
   \# KL terms material & \# KL terms load & PC order displacement& Total \# terms per DoF\\ \hline
   4 & 4 & 10 & 43,758 \\  
   4 & 4 & 20 & 3,108,105 \\    
   4 & 4 & 30 & 48,903,492 \\  
   6 & 6 & 10 & 646,646 \\    
   6 & 6 & 20 & 225,792,840 \\  
%   6 & 6 & 30 & 1.1058 $10^{10}$ \\    
%   8 & 8 & 10 & 5 311 735 \\  
%   8 & 8 & 20 & 7.3079 $10^{9}$ \\    
%   8 & 8 & 30 & 9.9149 $10^{11}$\\  
    ...  & ... & ... & ...\\   
%    \hline
  \end{tabular}}


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\begin{frame}
\frametitle{SEPFEM: Example in 1D}


\vspace*{-2mm}
\begin{center}
% \hspace*{-15mm}
\movie[label=show3,width=9cm,poster,autostart,showcontrols]
{\includegraphics[width=9cm]{/home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Latex/img/figure_elastic_900.png}}
% /home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Latex/img/figure_PEP_25.pdf
%{/home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Animations/SEPFEM_Animation_Elastic.mp4}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Probabilistic_Elasto_Plasticity_and_Stochastic_Elastic_Plastic_Finite_Element_Method/SEPFEM_Animation_Elastic.mp4}
\end{center}

% \includegraphics[width = 12cm]{./img/figure_elastic_900.pdf}




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\section{Conclusion}



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\begin{frame}
  \frametitle{Summary}

  \begin{itemize}

\vspace*{2mm}
    \item Numerical modeling to predict and inform, rather than fit

\vspace*{4mm}
    \item Engineer needs to know

\vspace*{4mm}
    \item Model, simulate and understand full life cycle of an object

%\vspace*{4mm}
%    \item Education and Training is the key!

\vspace*{4mm}
    \item  Funding  from  and  collaboration  with  the US-DOE, US-NRC, US-NSF, 
    US-BR, US-FEMA CNSC-CCSN, UN-IAEA, and Shimizu Corp. is greatly appreciated,

\vspace*{4mm}
    \item More info: \hspace*{3mm}  {\bf \url{http://real-essi.info/}}
      
\end{itemize}

\end{frame}
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\end{document}

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